Project Network-based Data Analysis
Annalisa Xamin
Data selection
The analysis will use the dataset GSE20437 obtained from GEO.The dataset is generated from Affymetrix HU133A microarrays and contains 42 tissue samples.
In detail, the data includes:
18 reduction mammoplasty (RM) breast epithelium samples,
18 histologically normal (HN) epithelial samples from breast cancer patients (9 ER+ and 9 ER-), and
6 histologically normal epithelial samples from prophylactic mastectomy patients.
Note that sample numbers correspond to individual patient samples.
# download the GSE20437 expression data series
#gse <- getGEO("GSE20437", destdir= './data/', getGPL = F)
# load the local copy of the data
gse <- getGEO(file = "./data/GSE20437_series_matrix.txt.gz", getGPL = FALSE)# getGEO returns a list of expression objects, but...
length(gse) ## [1] 1# shows us there is only one object in it.
# We assign it to the same variable.
#gse <- gse[[1]] # run only if you download data and
# if you don't use the local copy# extract metadata
metadata <- data.frame(gse@phenoData@data)expr(gse[1])## gse[1]Annotation of probesets from a GEO dataset to gene symbols
For the later analysis, it is useful to annotate the probe sets of the GEO data set to gene symbol. To do that, first we extract the name of the probes and then, we perform the annotation using biomaRt.
id_to_annotate <- rownames(gse@assayData[["exprs"]])
# extract id to annotate
# annotation
mart <- useMart("ENSEMBL_MART_ENSEMBL")
mart <- useDataset("hsapiens_gene_ensembl", mart)
annotLookup <- getBM(
mart = mart,
attributes = c(
"affy_hg_u133_plus_2",
"ensembl_gene_id",
"gene_biotype",
"external_gene_name",
"description"),
filter = "affy_hg_u133_plus_2",
values = id_to_annotate,
uniqueRows=TRUE)head(annotLookup)indicesLookup <- match(rownames(gse@assayData[["exprs"]]), annotLookup$affy_hg_u133_plus_2)
#head(annotLookup[indicesLookup, "external_gene_name"])dftmp <- data.frame(rownames(gse@assayData[["exprs"]]),
annotLookup[indicesLookup,
c("affy_hg_u133_plus_2", "external_gene_name")])
head(dftmp, 20)length(rownames(gse@assayData[["exprs"]]))## [1] 22283table(dftmp[,1] == dftmp[,2])##
## TRUE
## 20259Explore the groups in the dataset
p <- ggplot(metadata, aes(x=disease.state.ch1, fill=specimen.ch1))+
geom_bar()+
scale_fill_manual(values = my_colors[c(1,4,6,7)])
p + labs(x = "Group") 
Exploratory analysis
# show what we have:
show(gse)## ExpressionSet (storageMode: lockedEnvironment)
## assayData: 22283 features, 42 samples
## element names: exprs
## protocolData: none
## phenoData
## sampleNames: GSM512539 GSM512540 ... GSM512580 (42 total)
## varLabels: title geo_accession ... tissue:ch1 (38 total)
## varMetadata: labelDescription
## featureData: none
## experimentData: use 'experimentData(object)'
## pubMedIds: 20197764
## Annotation: GPL96The actual expression data are accessible in the exprs
section of gse, an Expression Set and the generic data
class that BioConductor uses for expression data.
head(exprs(gse)) ## GSM512539 GSM512540 GSM512541 GSM512542 GSM512543 GSM512544 GSM512545 GSM512546 GSM512547 GSM512548 GSM512549
## 1007_s_at 2461.4 3435.7 1932.5 2377.7 3055.3 2978.1 2348.5 2963.9 2776.9 3088.9 3033.3
## 1053_at 26.7 159.0 31.2 140.7 69.9 98.5 37.0 59.9 86.7 107.2 64.0
## 117_at 82.6 243.4 150.2 95.1 209.3 103.4 91.2 168.4 162.7 203.2 143.7
## 121_at 942.3 897.5 840.8 870.9 685.4 791.8 886.5 954.2 843.1 775.3 847.6
## 1255_g_at 71.8 87.9 75.4 58.1 31.8 40.3 70.5 43.3 51.6 42.6 74.9
## 1294_at 630.2 571.4 346.3 679.9 1289.3 421.1 417.6 811.6 778.1 393.2 995.4
## GSM512550 GSM512551 GSM512552 GSM512553 GSM512554 GSM512555 GSM512556 GSM512557 GSM512558 GSM512559 GSM512560
## 1007_s_at 3037.1 3545.8 3322.6 1963.7 3609.6 2078.9 4138.6 4260.7 2453.6 2709.0 2612.5
## 1053_at 82.9 97.7 69.7 82.0 45.6 84.5 31.7 37.4 82.4 204.8 119.3
## 117_at 113.5 80.0 186.4 106.6 145.6 144.4 133.6 278.6 173.0 147.8 186.0
## 121_at 912.2 911.6 862.4 705.0 984.6 853.8 846.8 1273.0 833.6 908.1 806.2
## 1255_g_at 53.7 30.5 15.2 42.5 76.6 88.2 90.6 65.8 25.8 77.5 84.3
## 1294_at 987.7 938.5 924.6 480.8 1054.1 632.0 448.0 1345.2 1248.9 405.7 647.5
## GSM512561 GSM512562 GSM512563 GSM512564 GSM512565 GSM512566 GSM512567 GSM512568 GSM512569 GSM512570 GSM512571
## 1007_s_at 4340.1 3155.3 2390.3 2738.8 3233.1 2836.6 2915.4 3457.5 2798.7 4370.2 2467.3
## 1053_at 76.7 100.3 115.4 14.1 47.6 77.1 47.1 47.0 83.2 40.2 80.3
## 117_at 168.0 95.2 73.6 122.7 107.6 120.9 143.4 92.5 72.1 131.8 156.4
## 121_at 827.0 629.4 709.2 305.6 877.4 425.7 643.8 771.3 681.1 812.7 533.4
## 1255_g_at 87.9 44.6 59.3 12.0 82.1 59.2 62.2 28.3 97.6 8.1 17.9
## 1294_at 2218.1 1321.1 606.7 1709.9 980.8 1268.4 955.8 1157.5 888.6 1130.8 905.1
## GSM512572 GSM512573 GSM512574 GSM512575 GSM512576 GSM512577 GSM512578 GSM512579 GSM512580
## 1007_s_at 3669.5 3310.1 3942.2 4520.4 3596.1 2989.0 3164.5 2764.3 4258.5
## 1053_at 24.1 8.8 44.6 54.7 56.7 89.9 63.4 57.0 59.5
## 117_at 165.8 141.6 97.1 132.7 124.3 210.5 131.4 89.6 123.3
## 121_at 746.9 1090.3 1008.7 718.6 988.4 295.9 957.3 630.8 869.2
## 1255_g_at 53.0 39.9 11.0 50.2 60.0 34.3 33.5 61.7 50.4
## 1294_at 1138.5 483.0 1326.5 1179.4 668.3 863.2 1055.5 1287.6 1127.8To conveniently access the data rows and columns present in
exprs(gse), this matrix is assigned to its own variable
ex.
# exprs (gse) is a matrix that we can assign to its own variable, to
# conveniently access the data rows and columns
ex <- exprs(gse)
dim(ex) # 42 sample, 22283 genes## [1] 22283 42The dataset contains gene expression data of 22283 genes (rows) from 42 patients (columns).
Pre-processing
# Analyze value distributions
boxplot(ex, main = 'Boxplot of the data before normalization',
xlab = "Samples",
ylab = "Expression Value",
varwidth = TRUE
)
The boxplot shows that scaling is necessary. So, in this case, I try to apply a log transformation to the data.
ex2<-log(ex)
ex2 <- na.omit(as.matrix(ex2))
#dim(ex2) # 22283 42 same as before
boxplot(ex2, main = 'Boxplot of the data after applying a logarithmic transformation',
xlab = "Samples",
ylab = "Expression Value"
)
Boxplot of the data after applying a logarithmic transformation
From the boxplot after the log transformation, I can see that there is some variation in the median of the samples. So, one of the simplest normalization strategies is to align the log values so that all channels have the same median. A convenient choice is zero so that positive or negative values reflect signals above or below the median for a particular channel.
normalized.log.ex=scale(log(ex))
# boxplot post median normalization on ex
boxplot(normalized.log.ex,
main = 'Boxplot of the data after median normalization',
xlab = "Samples",
ylab = "Expression Value")
PCA
PCA is a dimensionality reduction technique that allows to condense thousands of dimensions into just two or three.For the dataset’s samples, the PCA scores display the coordinates in relation to these additional dimensions.
pca <- prcomp(t(normalized.log.ex))
summary(pca)## Importance of components:
## PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8 PC9 PC10 PC11
## Standard deviation 21.6856 12.78817 11.18542 10.68629 10.28318 9.05796 8.85994 8.67632 8.31063 7.98169 7.80143
## Proportion of Variance 0.1798 0.06253 0.04783 0.04366 0.04043 0.03137 0.03001 0.02878 0.02641 0.02436 0.02327
## Cumulative Proportion 0.1798 0.24232 0.29016 0.33382 0.37425 0.40561 0.43563 0.46441 0.49081 0.51517 0.53844
## PC12 PC13 PC14 PC15 PC16 PC17 PC18 PC19 PC20 PC21 PC22 PC23
## Standard deviation 7.64884 7.42525 7.35447 7.25191 7.12698 7.03899 6.96990 6.86700 6.81828 6.7261 6.71031 6.59828
## Proportion of Variance 0.02237 0.02108 0.02068 0.02011 0.01942 0.01894 0.01857 0.01803 0.01777 0.0173 0.01722 0.01665
## Cumulative Proportion 0.56081 0.58189 0.60257 0.62267 0.64209 0.66104 0.67961 0.69764 0.71541 0.7327 0.74993 0.76657
## PC24 PC25 PC26 PC27 PC28 PC29 PC30 PC31 PC32 PC33 PC34 PC35
## Standard deviation 6.51084 6.39868 6.39565 6.35069 6.16713 6.14788 6.07658 6.01840 5.86441 5.80650 5.71226 5.62268
## Proportion of Variance 0.01621 0.01565 0.01564 0.01542 0.01454 0.01445 0.01412 0.01385 0.01315 0.01289 0.01248 0.01209
## Cumulative Proportion 0.78278 0.79843 0.81407 0.82949 0.84403 0.85848 0.87260 0.88645 0.89960 0.91249 0.92496 0.93705
## PC36 PC37 PC38 PC39 PC40 PC41 PC42
## Standard deviation 5.46227 5.35021 5.28516 5.20027 5.10709 5.01262 4.456e-14
## Proportion of Variance 0.01141 0.01094 0.01068 0.01034 0.00997 0.00961 0.000e+00
## Cumulative Proportion 0.94846 0.95940 0.97008 0.98042 0.99039 1.00000 1.000e+00screeplot(pca)
To get the summary of the PCA and the plot showing the variance explained by the first 10 components, it is possible to use the functions commented in the chunks above.
However, using ggplot2 and factoextra
packages is possible to get a more concise and informative plot
reporting the same information.
pcaVar <- get_eig(pca)
pcaVar <- pcaVar$variance.percent[1:10]
screeDf <- data.frame("Dimensions" = as.factor(seq(1,10)),
"Percentages" = pcaVar,
"Labels" = paste(round(pcaVar, 2), "%"))
p <- ggplot(data = screeDf, aes(x=Dimensions, y=Percentages))+
geom_bar(stat = "identity", fill = "#d1105a")+
geom_text(aes(label=Labels), vjust=-0.5, color="black", size=3.6)+
ggtitle("Scree Plot")+
ylab("Percentage of variance explained")+
scale_x_discrete(labels = as.factor(seq(1,10)))
p
The scree plot shows that the first dimensions on the left are the more important because the percentage of variance explained by them is higher. The remaining principal components account for a very small proportion of the variability and are probably unimportant.
Let’s try to plot the PCA, looking if we can see a separation between Control and Breast Cancer groups.
# draw PCA plot control VS breast cancer
group <- c(rep("cadetblue1",18), rep("red",18), rep("cadetblue1",6) )
plot(pca$x[,1], pca$x[,2], xlab="PCA1", ylab="PCA2", main="PCA for components 1 and 2", type="p", pch=10, col=group)
text(pca$x[,1], pca$x[,2], rownames(pca$data), cex=0.75)
legend("topleft", col=c("cadetblue1","red"), legend = c("Control", "Breast Cancer"),
pch = 20, bty='n', cex=.55)
Let’s try to add the control subtypes. The vector group used in the PCA plot is based on the data. The samples corresponding to the colors are the following:
Light blue: reduction mammoplasty (RM) breast epithelium samples
Red: histologically normal (HN) epithelial samples from breast cancer patient
Purple: histologically normal breast epithelium (NlEpi) from prophylactic mastectomy patient samples
# draw PCA plot
group <- c(rep("cadetblue1",18), rep("red",18), rep("purple",6) ) # vector of colors based on the order of my data
plot(pca$x[,1], pca$x[,2], xlab="PCA1", ylab="PCA2", main="PCA for components 1 and 2", type="p", pch=10, col=group)
text(pca$x[,1], pca$x[,2], rownames(pca$data), cex=0.75)
legend("topleft", col=c("cadetblue1","red","purple"), legend = c("Reduction Mammoplasty", "Breast Cancer", "Prophylactic Mastectomy"),
pch = 20, bty='n', cex=.55)
Then, I try to see if there is a separation also inside different types of Breast Cancer.
# draw PCA plot with all subtypes
group <- c(rep(my_colors[7],18), rep(my_colors[4],9), rep(my_colors[1],9), rep(my_colors[6],6) ) # vector of colors based on the order of my data
plot(pca$x[,1], pca$x[,2], xlab="PCA1", ylab="PCA2", main="PCA for components 1 and 2", type="p", pch=10, col=group)
text(pca$x[,1], pca$x[,2], rownames(pca$data), cex=0.75)
legend("topleft", col=c(my_colors[7],my_colors[4],my_colors[1],my_colors[6]), legend = c("Reduction Mammoplasty", "ER+ Breast Cancer", "ER- Breast Cancer", "Prophylactic Mastectomy"),
pch = 20, bty='n', cex=.55)
Interactive PCA plot
Let’s try to explore an interactive PCA plot.
components<-pca[["x"]]
components<-data.frame(components)
type<-c(rep("RM", 18), rep("HN",18), rep("NlEpi",6))
components<-cbind(components, type )
fig <- plot_ly(components, x=~PC1, y=~PC2,
color=type,colors=c('cadetblue1', 'red','purple'),
type='scatter',mode='markers')
figfig2 <- plot_ly(components, x=~PC1, y=~PC2, z=~PC3,
color=type, colors=c('cadetblue1', 'red','purple'),
mode='markers', marker = list(size = 4))
fig2fig3 <- plot_ly(components, x=~PC1, y=~PC3,
color=type, colors=c('cadetblue1', 'red','purple'),
type='scatter',mode='markers')
fig3set.seed(123)
umap_result <- umap(t(normalized.log.ex))
umap_df <- as.data.frame(umap_result$layout)
colnames(umap_df) <- c("UMAP1", "UMAP2")
# Add sample types to the UMAP data frame
umap_df$type <- c(rep("RM", 18), rep("HN",18), rep("NlEpi",6))
ggplot(umap_df, aes(x = UMAP1, y = UMAP2, color = type)) +
geom_point(size = 3, alpha = 0.8) +
scale_color_manual(values = c("RM" = "cadetblue1",
"HN" = "red",
"NlEpi" = "purple")) +
theme_minimal() +
labs(title = "2D UMAP Projection of GSE20437", x = "UMAP1", y = "UMAP2")
Clustering
K-means
set.seed(1)
k <- 2 # number of clusters
kmeans_result <- kmeans(t(normalized.log.ex),k)
table(kmeans_result$cluster) # tells how many samples were assigned to each cluster##
## 1 2
## 14 28plot(kmeans_result, data=t(normalized.log.ex)) + geom_text(aes(label=metadata$disease.state.ch1),hjust=0,vjust=0)
fviz_cluster(kmeans_result, data = t(normalized.log.ex),
palette = c("#FF6666", "#33cccc"),
geom = "point",
ellipse.type = "convex",
ggtheme = theme_bw()
)
Let’s try increasing the number of clusters.
set.seed(1)
k <- 4 # number of clusters
kmeans_result <- kmeans(t(normalized.log.ex),k)
table(kmeans_result$cluster) # tells how many samples were assigned to each cluster##
## 1 2 3 4
## 4 7 10 21plot(kmeans_result, data=t(normalized.log.ex)) + geom_text(aes(label=metadata$specimen.ch1),hjust=0,vjust=0)
fviz_cluster(kmeans_result, data = t(normalized.log.ex),
palette = c("#FF6666", "#99C666", "#33cccc", "#cc66ff"),
geom = "point",
ellipse.type = "convex",
ggtheme = theme_bw()
)
Hierarchical
# Elbow method
fviz_nbclust(t(normalized.log.ex), FUN = hcut, method = "wss") 
## seems setting number of clusters equal to 2# Silhouette method
fviz_nbclust(t(normalized.log.ex), FUN = hcut, method = "silhouette")
## seems setting number of clusters equal to 2We use the Gap statistic to calculate the goodness of clustering.
# Gap Statistic Method
gap_stat <- clusGap(t(normalized.log.ex), FUN = hcut, nstart = 25, K.max = 10, B = 50)
# K.max -> the maximum number of clusters to consider
# B -> number of Monte Carlo samples
fviz_gap_stat(gap_stat)
hc_result <- dist(t(normalized.log.ex)) %>% hclust(method = "ave")
hc_result2<- dist(t(normalized.log.ex), method="euclidean") %>% hclust( method = "complete")
hc_result3 <- dist(t(normalized.log.ex)) %>% hclust(method = 'single')
k_hc <- 2 # optimal number of clusters
groups <- cutree(hc_result, k=k_hc)
table(groups,type)## type
## groups HN NlEpi RM
## 1 17 6 18
## 2 1 0 0groups2<-cutree(hc_result2, k=k_hc)
table(groups2,type)## type
## groups2 HN NlEpi RM
## 1 4 0 10
## 2 14 6 8groups3 <- cutree(hc_result3,k=k_hc)
table(groups3,type)## type
## groups3 HN NlEpi RM
## 1 17 6 18
## 2 1 0 0# Set up layout with extra space below the plot
par(mar = c(6, 4, 4, 2)) # increase bottom margin
par(xpd = TRUE) # allow text outside plot region
# Plot dendrogram
plot(hc_result, hang = -1, labels = type,
main = 'Hierarchical clustering dendrogram (average)')
rect.hclust(hc_result, k = 2, border = 2) # red boxes to show groups
# Add custom legend box below the plot
text(x = mean(par("usr")[1:2]), y = par("usr")[3] - 10,
labels = paste(
"RM = Reduction Mammoplasty breast epithelium\n",
"HN = Histologically normal epithelial samples from breast cancer patients (ER+ and ER-)\n",
"NlEpi = Normal epithelial samples from prophylactic mastectomy patients"
),
cex = 0.8, adj = 0.5)
# Set up layout with extra space below the plot
par(mar = c(6, 4, 4, 2)) # increase bottom margin
par(xpd = TRUE) # allow text outside plot region
# Plot dendrogram
plot(hc_result2, hang = -1, labels = type,
main = 'Hierarchical clustering dendrogram (complete)')
rect.hclust(hc_result, k = 2, border = 2) # red boxes to show groups
# Add custom legend box below the plot
text(x = mean(par("usr")[1:2]), y = par("usr")[3] - 10,
labels = paste(
"RM = Reduction Mammoplasty breast epithelium\n",
"HN = Histologically normal epithelial samples from breast cancer patients (ER+ and ER-)\n",
"NlEpi = Normal epithelial samples from prophylactic mastectomy patients"
),
cex = 0.8, adj = 0.5)
# Set up layout with extra space below the plot
par(mar = c(6, 4, 4, 2)) # increase bottom margin
par(xpd = TRUE) # allow text outside plot region
# Plot dendrogram
plot(hc_result3, hang = -1, labels = type,
main = 'Hierarchical clustering dendrogram (single)')
rect.hclust(hc_result, k = 2, border = 2) # red boxes to show groups
# Add custom legend box below the plot
text(x = mean(par("usr")[1:2]), y = par("usr")[3] - 10,
labels = paste(
"RM = Reduction Mammoplasty breast epithelium\n",
"HN = Histologically normal epithelial samples from breast cancer patients (ER+ and ER-)\n",
"NlEpi = Normal epithelial samples from prophylactic mastectomy patients"
),
cex = 0.8, adj = 0.5)
Random forest
set.seed(1234)
rf <- randomForest(x=t(normalized.log.ex), y=as.factor(type), ntree=1000)
plot(rf, main = "Random Forest")
The plot above shows how the error rate changes according to the number of trees. This allows to track how model accuracy improves (or doesn’t) as more trees are added. The black line represent the overall OOB (out-of-bag) error rate, while the other colored lines report the class specific error rates.
# a trivial test
predict(rf, t(normalized.log.ex[, 1:5]))## GSM512539 GSM512540 GSM512541 GSM512542 GSM512543
## RM RM RM RM RM
## Levels: HN NlEpi RM# Get importance values
rf_importance <- importance(rf)
# Extract probe IDs in order of importance
ordered_probes <- rownames(rf_importance)[order(rf_importance[, 1], decreasing = TRUE)]
# Ensure correct mapping exists
probe_to_symbol <- annotLookup[, c("affy_hg_u133_plus_2", "external_gene_name")]
colnames(probe_to_symbol) <- c("probe", "symbol")
probe_symbols <- setNames(probe_to_symbol$symbol, probe_to_symbol$probe)
top_vars <- head(ordered_probes, 30) # Show top 30 features
imp_df <- data.frame(
probe = top_vars,
importance = rf_importance[top_vars, 1],
gene = ifelse(top_vars %in% names(probe_symbols), probe_symbols[top_vars], top_vars)
)
ggplot(imp_df, aes(x = reorder(gene, importance), y = importance)) +
geom_bar(stat = "identity", fill = "#2e005d") +
coord_flip() +
labs(title = "Top 30 Variable Importance (Random Forest)", x = "Gene", y = "Importance") +
theme_minimal(base_size = 12)
Heatmap
This is optional. Not suggested to include heatmap in the report, because at the end of the project there will be too many graphs and this is not a valuable one.
# Select top N important probes
top_n <- 30
top_probes <- imp_df$probe[1:top_n]
heatmap_data <- normalized.log.ex[top_probes, ]
# Add gene symbols
gene_symbols <- imp_df$gene[1:top_n]
rownames(heatmap_data) <- gene_symbols
pheatmap(heatmap_data,
scale = "row", # normalize expression within each gene
clustering_distance_rows = "euclidean",
clustering_distance_cols = "euclidean",
clustering_method = "complete",
show_rownames = TRUE,
show_colnames = TRUE,
fontsize_row = 8,
main = "Top Random Forest Genes Heatmap")
# Ensure sample labels are aligned with expression data
sample_types <- metadata$type
names(sample_types) <- colnames(normalized.log.ex)
# Subset for current samples
sample_types <- sample_types[colnames(heatmap_data)]
# Set rownames to match sample IDs
rownames(metadata) <- metadata$geo_accession
# Create annotation dataframe
annotation_col <- data.frame(Type = metadata[colnames(heatmap_data), "specimen.ch1"])
rownames(annotation_col) <- colnames(heatmap_data)
# Convert to factor
annotation_col$Type <- factor(annotation_col$Type)
type_levels <- levels(annotation_col$Type)
palette_colors <- brewer.pal(n = length(type_levels), name = "Set2") # or "Dark2", "Paired", etc.
names(palette_colors) <- type_levels
ann_colors <- list(Type = palette_colors)
pheatmap(heatmap_data,
scale = "row",
annotation_col = annotation_col,
annotation_colors = ann_colors,
show_colnames = TRUE,
main = "Heatmap Top Random Forest Genes by Specimen")